Wkład UE:

Kraj koordynujący:

Topic(s):

Zaproszenie do składania wniosków:

System finansowania:

MC-IRG - International Re-integration Grants (IRG)

Cel

Singularly perturbed systems are ubiquitous in mathematics and its applications. These problems often appear due to a time scaleseparation i.e. when two processes evolve at substantially different rates. The goal of this project is to advance the theory of multiple timescale systems in the following directions.(1) Mixed-mode oscillations: These complicated oscillatory patterns appear in a wide range of models. In particular, high-dimensionalproblems are of interest.(2) Multiparameter problems: Bifurcation theory of mulitscale systems, particularly for two or more singular parameters, has to bedeveloped. A starting point are two-parameter bifurcation curves in the FitzHugh-Nagumo equation.(3) Geometric de-singularization: Extension and development of the so-called blow-up method are a major part of this project.(4) Extension of current methods: A further driving question will be how the theory for finite-dimensional systems extends to stochastic andpartial differential equations; even the understanding of simple examples is anticipated to very interesting.